Integrals of Rational Functions
has everything you need to know.
you can search for "How to evaluate an improper integral with a contour integral." to skip directly to it.
Does any body know how to go about doing the following Integrals using complex contour integration (upper half semicircle contour):
1) Integrate from 0 to infinity 1/(2+x+x^3) dx
2) Integrate from 1 to infinity 1/(x*sqrt(x^2-1)) dx
I had a look at that site....very helpful,but the integral I posted: Integral 0 to infinity 1/(2+x+x^3) is an odd integrand,so cant use a semicircle contour.I couldn't find anything on that site when dealing with an odd integrand
What contour should I use for this problem? I have tried using a sector but couldn't get it to work...